报告人：顾玲琪博士 维也纳大学
报告题目：Stability of utility maximization problems in the market with bounded random endowments and transaction costs.
时 间：2016年12月16日 (星期五) 14:00 ~ 15:00
地 点：旗山校区理工1号楼统计实验室
主 办：数学与计算机科学学院, 福建省分析数学及应用重点实验室，数学研究中心
参加对象：相关专业教师和学生
报告摘要：We consider the dual problem of expected utility maximization problems in markets
with/without transaction costs, especially the property of optimal dual processes which produce the unique dual optimizer (solution) to the dual problem.
Even in incomplete semimartingale market, in general, the unique optimal dual process is not a local martingale but a supermartingale. However, if the stock price is a continuous semimartingale, then the optimal dual process is a local martingale. This result can be extended to the case with bounded random endowment. Precisely, the countably additive part of the dual optimizer obtained by Cvitanic, Schachermayer, Wang in 2001 can be attained by a local martingale, which is a supermartingale deator defined by Kramkov and Schachermayer in 1999, when the underlying ltration is generated by Brownian motion.
Then we discuss such problem in markets with transaction costs. Under sufficient condition of the strict positivity of liquidation value process of an optimal trading strategy, all optimal dual processes (may not be unique) are local martingales. Then, we consider the convergence of optimal dual processes and shadow price processes by assuming the continuity of the stock price process, after having acquired static stability of the utility maximization problem.
The talk is based on the paper of L. GU, Y. Lin, J. Yang (2016): On the dual problem of utility maximization in incomplete market (stochastic processes and their applications) and a working paper called stability of utility maximization problems in markets with transaction costs.
专家简介：维也纳大学数学学院金融数学博士研究生。
